d\)' 



318 Mr Filon, On the variation ivith the wave-length 



CLOG Uj\> 



But here — = — — (neglecting the small change in 0), so that 



CO A- 



_ 2p 2 W7r / \ dA 

 y 3" { 2AdX 

 approximately. 



Hence the proportional error in % is 

 p 2 / _l\dA 

 ~3\ 22 



\ dA 



Now —r -j— is the ratio of the. proportional change in intensity 

 A d\ 



to the corresponding proportional change in wave-length. Apart 

 from the fact that, in estimating the blackness of a band, the eye 

 compares with the intensity of the original field in that neighbour- 

 hood, rather than with an absolute standard, it seems unlikely 

 that a change of 5 tenth-metres can anywhere (except perhaps 

 right at the very ends of the range of visibility) imply more than 

 1 per cent, change in the intensity : so that about ^ per cent, of 



X to 1 per cent, of A, or -j ,— = 10 numerically, appears an 



jA. a\ 



extreme estimate. 



5. The following experiments were undertaken with the view 

 of obtaining the order of the error introduced in this way. 

 A line vertical slit was placed, first at one edge of the block and 

 then at the other, and readings of the black band were taken for 

 these two positions of the slit. 



They gave : 



reading approximate \ 



Slit at right-hand edge 48° 30' 4300 



„ „ left „ „ 46° 34' 5000 



Distance between centres of slit in the two positions = 9 mm. 

 roughly. 



Assuming the stress-optical coefficient to be roughly constant 

 over this range of X, the extreme stresses are nearly in the ratio 

 43 : 50. 



Therefore 



change in stress for 9 mm. _ 7 _ 14 

 stress in middle /43 + 50 \ 93 ' 



{— 2~ ) 



change in stress per mm._$__14_l . 



^stress in middle ~T~ 837 = 60 n y< 



